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Precision Least Squares: Estimation and Inference in High-Dimensions

Margaritella, Luca LU and Sessinou, Rosnel (2025) In Journal of Business & Economic Statistics
Abstract
The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be approximately Gaussian, efficient, and to provide automatic family-wise error control in large samples. For estimating high-dimensional sparse regression models, we propose a LASSO Cholesky estimator of the plug-in precision matrix. We show its consistency and how to properly... (More)
The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be approximately Gaussian, efficient, and to provide automatic family-wise error control in large samples. For estimating high-dimensional sparse regression models, we propose a LASSO Cholesky estimator of the plug-in precision matrix. We show its consistency and how to properly bias correct it, thereby obtaining a LASSO Cholesky-based PrLS (LC-PrLS) estimator. LC-PrLS performs well in finite samples and better than state-of-the-art high-dimensional estimators. We employ LC-PrLS to investigate the dynamic network of predictive connections among a large set of global bank stock returns. We find that crisis years correspond to a collapse of predictive linkages. (Less)
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type
Contribution to journal
publication status
published
subject
keywords
Precision Least Squares, High-Dimensional Inference, Predictive Networks, C32, C55, C12, G19
in
Journal of Business & Economic Statistics
publisher
Taylor & Francis
external identifiers
  • scopus:85217036888
ISSN
1537-2707
DOI
10.1080/07350015.2024.2440573
language
English
LU publication?
yes
id
3e85f58a-ccb6-44ed-b39d-1c53e70661ed
date added to LUP
2024-12-17 16:10:48
date last changed
2025-10-14 12:44:46
@article{3e85f58a-ccb6-44ed-b39d-1c53e70661ed,
  abstract     = {{The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be approximately Gaussian, efficient, and to provide automatic family-wise error control in large samples. For estimating high-dimensional sparse regression models, we propose a LASSO Cholesky estimator of the plug-in precision matrix. We show its consistency and how to properly bias correct it, thereby obtaining a LASSO Cholesky-based PrLS (LC-PrLS) estimator. LC-PrLS performs well in finite samples and better than state-of-the-art high-dimensional estimators. We employ LC-PrLS to investigate the dynamic network of predictive connections among a large set of global bank stock returns. We find that crisis years correspond to a collapse of predictive linkages.}},
  author       = {{Margaritella, Luca and Sessinou, Rosnel}},
  issn         = {{1537-2707}},
  keywords     = {{Precision Least Squares; High-Dimensional Inference; Predictive Networks; C32; C55; C12; G19}},
  language     = {{eng}},
  publisher    = {{Taylor & Francis}},
  series       = {{Journal of Business & Economic Statistics}},
  title        = {{Precision Least Squares: Estimation and Inference in High-Dimensions}},
  url          = {{http://dx.doi.org/10.1080/07350015.2024.2440573}},
  doi          = {{10.1080/07350015.2024.2440573}},
  year         = {{2025}},
}